Sure it will, if you add an odd key to another odd key ( our 2^256 key is odd ) you'll get an even key and all you have to do is to subtract the following key from the result :
But why bother if you could add or subtract 1G from your odd key and divide it without having to do what I said.

You can always divide an odd key, if by 2, you'd have to add n/2 to the result, if by 3, adding n/3 etc to get your actual and correct result.